Well, the computer is back to normal (more or less). Thanks to those who offered advice - I did end up taking it to a techie, and several days (and $250) later, I have a working system once again.

I turned out that not only did it have a virus (possibly more than one), one of the memory sticks had gone bad. Getting the 512mb stick replaced with a shiny new 1GB one resolved the problem, and as a bonus I now have an extra half-gig of memory to play with.

Now I'm in the process of re-installing all of my apps, and restoring my files from backups. Speaking of backups, those USB thumb drives are a good investment - I picked up a 16GB model for $55, and it had room for pretty much everything I had on my computer (including emails - I'm something of a digital pack-rat), with space left over. I'll probably invest in a portable hard drive next - about $100 for a 250GB model.